Detection of characteristic phases using FFT´s

Maximal-length linear recursive sequences (M-sequences) over GF(2) are used for a variety of purposes in communications, test, and other signals. An M-sequence contains a unique characteristic phase at which the sequence is invariant under a decimation by two. This point may be detected using an algorithm whose principal computation is the fast Fourier transform (FFT). This approach provides a method of detecting and synchronizing to the sequence, regardless of whether the sequence is at baseband or modulates a carrier, the relationship of sampling rate to bit rate, and whether the modulated sequence is regarded as a carrier which itself modulates a small-bandwidth, constant envelope signal. Moreover, the technique provides a method for obtaining the polynomial generator of the sequence if it is not already known